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We study the statistics of velocity circulation in two-dimensional classicaland quantum turbulence. We perform numerical simulations of the incompressibleNavier-Stokes and the Gross-Pitaevskii (GP) equations for the direct andinverse cascades. Our GP simulations display clear energy spectra compatiblewith the double cascade theory of two-dimensional classical turbulence. In theinverse cascade, we found that circulation intermittency in quantum turbulenceis the same as in classical turbulence. We compare GP data to Navier-Stokessimulations and experimental data from [Zhu et al. Phys. Rev. Lett. 130,214001(2023)]. In the direct cascade, for nearly incompressible GP-flows,classical and quantum turbulence circulation displays the same self-similarscaling. When compressible effects become important, quasi-shocks generatequantum vortices and the equivalence of quantum and classical turbulence onlyholds for low-order moments. Our results establish the boundaries of theequivalence between two-dimensional classical and quantum turbulence.

Exploring the Equivalence between Two-dimensional Classical and Quantum Turbulence through Velocity Circulation Statistics